Flash calculation, vapor-liquid equilibrium

Illustrates use of subroutine FLASH for vapor-liquid equilibrium separation calculations for up to 10 components and of subroutine PARIN for parameter loading. 

An equilibrium-flash calculation (using the same equations as in case A above) is made at each point in time to find the vapor and liquid flow rates and properties immediately after the pressure letdown valve (the variables with the primes F , F l, y], x j,.. . shown in Fig. 3.8). These two streams are then fed into the vapor and liquid phases. The equations describing the two phases will be similar to Eqs. (3.40) to (3.42) and (3.44) to (3.46) with the addition of (1) a multi-component vapor-liquid equilibrium equation to calculate Pi and (2) NC — 1 component continuity equations for each phase. Controller equations relating 1 to Fi and P to F complete the model. 

The proper design of distillation and absorption columns depends on knowledge of vapor—liquid equilibrium, as do flash calculations used to determine the physical state of streams at given conditions of temperature, pressure, and composition. Detailed treatments of vapor—liquid equilibria are available (6,7). 

Flash Calculations. The ability to carry out vapor-liquid equilibrium calculations under various specifications (constant temperature, pressure constant enthalpy, pressure etc.) has long been recognized as one of the most important capabilities of a simulation system. Boston and Britt ( 6) reformulated the independent variables in the basic flash equations to make them weakly coupled. The authors claim their method works well for both wide and narrow boiling mixtures, and this has a distinct advantage over traditional algorithms ( 7). 

One further vapor/liquid equilibrium problem is the flash calculation. origin of the name is in the change that occurs when a liquid under press passes through a valve to a pressure low enough that some of the liquid vapori or flashes, producing a two-phase stream of vapor and liquid in equilibri We consider here only the P.f -flash, which refers to any calculation of quantities and compositions of the vapor and liquid phases making up a two-ph system in equilibrium at known P, T, and overall composition. 

In most industrial processes coexisting phases are vapor and liquid, although liquid/liquid, vapor/solid, and liquid/solid systems are also encountered. In this chapter we present a general qualitative discussion of vapor/liquid phase behavior (Sec. 12.3) and describe the calculation of temperatures, pressures, and phase compositions for systems in vapor/liquid equilibrium (VLE) at low to moderate pressures (Sec. 12.4).t Comprehensive expositions are given of dew-point, bubble-point, and P, T-flash calculations. 

Thermodynamic calculations are used to evaluate vapor-liquid equilibrium constants, enthalpy values, dew points, bubble points, and flashes. Established techniques simulate the heat exchangers and distillation columns, and handle convergence and optimization. 

This chapter considers the vapor-liquid equilibrium of mixtures, conditions for bubble and dew points of gaseous mixtures, isothermal equilibrium flash calculations, the design of distillation towers with valve trays, packed tower design. Smoker s equation for estimating the number of plates in a binary mixture, and finally, the computation of multi-component recovery and minimum trays in distillation columns. 

The method described here is based on the vapor-liquid equilibrium relationships given in handbooks available from the Gas Processors Suppliers Association. This technique will handle flash calculations with feed streams containing up to 15 components. As an added feature, the calculation will check the feed composition at flash conditions for dew point or bubble point condition (i.e., whether the feed is either all vapor or all liquid). These checks are done before the flash calculations are started. If the feed is above the dew point or below the bubble point, an appropriate message is displayed on the computer screen. A default value for R (L/V) = 1.0 is used to start the iterative process. 

Using one of these activity coefficient equations it is possible to calculate liquid-liquid equihbrium (LLE) behavior of multicomponent hquid systems. Consider, for example, the ternary system of Figure 1. A system of overall composition A splits into two liquid phases B and C. The calculation of compositions of B and C is analogous to the flash ciculation of vapor-liquid equilibrium problems. By using the UNIQUAC equations to obtain the partition coefficients, Kj, this problem can be solved for any composition A of the overall system. The calculations are lengthy but computer programs for this purpose (2) have been published. In this paper simpler approximate methods for phase equilibrium problems of environmental interest is sought. For the moment it is sufficient to note that the activity coefficients provide the means of complete liquid-liquid equihbrium computations. 

BCnowledge of the vapor-liquid equilibrium (VLB) behavior in these mixtures is necessary to design and to optimize the separation in the flash vessel, which is part of the extractive process considered in this work, described in the next section. The problem of phase equilibrium consists on the calculation of some variables of the set T, P, x, and y) when some of them are known. 

A vapor-liquid equilibrium flash calculation is again carried out to obtain new fugacity values using Equation 15. The process of comparing fugacities and adjusting mixture composition is repeated until Equation 1 is satisfied and the SLV equilibrium condition is considered to have been found. 

First, we distinguished between an T and an T identification of state. Less information is provided by an IF-spedfication than by an F -specification, but in particular situations one or the other may be more appropriate. For example, in vapor-liquid equilibrium calculations, an IF-specification is sufficient to close a bubble-T problem, but an F -spedfication fails to dose an isothermal flash problem. Furthermore, most reaction-equilibrium problems are not dosed by F-spedfications they require F -specifications. We have also illustrated that in some situations an F-specification may be suffident, but an F -spedfication may lead to a more advantageous problem formulation and solution technique. The prindpal pitfall is to apply an F-specification to a problem that demands an F -spedfication, for then the problem is ill-posed. 

Consider a multicomponent mixture in vapor-liquid equilibrium let x represent the set of mole fractions for the liquid and let y be the same for the vapor. In a closed system, the compositions x] and y will change, often drastically, with changes in T and P. However, in many systems the ratio y, /x,-, for each component i, is less sensitive to changes of state than is either x,- or y,- by itself. This observation is exploited by introducing two quantities the K-factor and the relative volatility ( 12.1.2). We have already encountered the K-factor in the Rachford-Rice method for flash calculations see (11.1.24) and Problem 11.7. 

Chemical and industrial engineering both provide a series of examples involving nonideal vapor-liquid equilibrium calculation. For example, the equations governing a flash drum separator with molar fractions Zi, Z2, , Zc, flow rate F, and enthalpy H are... 

The single-stage membrane unit becomes equivalent to a so-called flash vaporization. The flash vaporization calculation itself is straightforward, with the vapor and liquid phases assumed at equilibrium, and is presented in a number of references." " The limits correspond to the dew-point and bubble-point calculations for vapor-liquid equilibrium, which are special or limiting cases for the flash vaporization calculation. It is the object, therefore, to adapt the membrane calculation to the techniques for the flash vaporization calculation and thereby take advantage of the relative simplicity of the latter. 

Flash Units. In simulators, the term flash refers to the module that performs a single-stage vapor-liquid equilibrium calculation. Material, energy, and phase equilibrium equations are solved for a variety of input parameter specifications. In order to specify completely the condition of the two output streams (liquid and vapor), two parameters must be input. Many combinations are possible—for exanple, temperature and pressure, temperature and heat load, or pressure and mole ratio of vapor to liquid in exit streams. Often, the flash module is a combination of two pieces of physical equipment, that is, a phase separator and a heat exchanger. These should appear as separate equipment on the PFD. Note that a flash unit can also be specified for batch operation, in which case the unit can serve as a surge or storage vessel. 

Vapor-Liquid-Liquid Equilibrium. We have had limited experi-lence in rigorous three phase equilibrium calculations, vapor-liquid-liquid, primarily in single stage flash units. The implementation of such a three-phase equilibrium model in column calculation is scheduled in the future. Presently, a method also exists wherein complete immisclhility in the liquid phase can be specified between one component and all of the other components in the system e.g., between water and a set of hydrocarbons. The VLE ratios are normalized on an overall liquid basis so that the results can be used in conventional two-phase liquid-vapor equilibrium calculations. 

Besides providing feasible computer routes to handle the three aforementioned problems, special care must be taken to prevent the computer flash algorithm from oscillating back and forth in K constant (vapor-liquid equilibrium) calculations because the prescribed flash conditions of temperature and pressure do not fall in the two-phase region. It would be presumptuous to assume that all flash conditions are realistic engineers do, and will continue to, submit unrealistic temperature and pressures, in the range of subcooled liquids and superheated vapors. 

These calculations combine vapor-liquid equilibrium relationships with total mass and component balances. Material of known composition Zj is fed into a flash drum at a known rate of F mols/min. Both the temperature and the pressure in the drum are given. Variables that are unknown are liquid and vapor compositions and liquid and vapor flow rates. See Figure 2.12. 

Example 6.3.1 A liquid mixture containing 12% ethane, 32% propane and 56% n-butane (see Example 4.1.1) is throttled into a flash drum at 32 °C and 700 kPa. The feed composition provided is in mole %. Calculate the fraction of the feed stream which leaves the flash drum as a vapor if vapor-liquid equilibrium may be assumed. Determine the compositions of the vapor stream and the liquid stream. Assume that the Kj values may be obtained from Figures 4.1.5 and 4.1.6. 

Solution The governing equations are (6.3.65), (6.3.55) and (6.3.54). First, one must make sure that the problem specifications are such that the flash drum conditions are in the two-phase region of vapor-liquid equilibrium. We calculate the value of /(lk, /Tiy) from equation (6.3.65) for two values of (lkft,/W((), namely 0 and 1. Consider (Tk, /1%) = 0 first. From Figure 4.1.6, we determine K, for the three species (see Table 6.3.2). 

The equilibrium distribution of a mixture of volatile liquids between a vapor phase and a liquid phase in a closed vessel was introduced in Sections 3.3.7.1 and 4.1.2 as the basis for tbe separation process of distillation. The preferential enrichment of the vapor phase with the more volatile species and the liquid phase with the less volatile species was illustrated in Section 4.1.2 for a variety of systems, along with the procedures for calculating the composition of each phase in a closed system. How chemical reactions in the liquid phase affect such vapor-liquid equilibrium was demonstrated in Section 5.2.I.2. In Section 6.3.2.1, open systems of flash vaporization and batch distillation in the context of bulk flow of the vapor and liquid phases parallel to the direction of the force were studied, and the separation achieved was quantified. The most common configuration of separation based on vapor-liquid equilibrium employs, however, a vertical column in which the vapor stream flows up and the liquid stream flows down. How the vapor and the liquid phases may contact each other was illustrated, for example, in Figure 2.1.2(b) for a... 

Under the assnmption of equilibrium conditions, and knowing the composition of the fluid stream coming into the separator and the working pressure and temperature conditions, we conld apply our current knowledge of vapor/liquid/equilibrium (flash calculations) and calculate the vapor and liquid fractions at each stage. 

Equilibrium separation involves the two-phase region between the two curves. Equihbrium calculations, often referred to as "flash calculations," are based upon a combination of the vapor— liquid equilibrium relationship and material balance equations. 

The calculation of single-stage equilibrium separations in multicomponent systems is implemented by a series of FORTRAN IV subroutines described in Chapter 7. These treat bubble and dewpoint calculations, isothermal and adiabatic equilibrium flash vaporizations, and liquid-liquid equilibrium "flash" separations. The treatment of multistage separation operations, which involves many additional considerations, is not considered in this monograph. 

In modern separation design, a significant part of many phase-equilibrium calculations is the mathematical representation of pure-component and mixture enthalpies. Enthalpy estimates are important not only for determination of heat loads, but also for adiabatic flash and distillation computations. Further, mixture enthalpy data, when available, are useful for extending vapor-liquid equilibria to higher (or lower) temperatures, through the Gibbs-Helmholtz equation. ... 

The same fundamental development as presented here for vapor-liquid flash calculations can be applied to liquid-liquid equilibrium separations. In this case, the feed splits into an extract at rate E and a raffinate at rate R, which are in equilibrium with each other. The compositions of these phases are... 

It is important to stress that unnecessary thermodynamic function evaluations must be avoided in equilibrium separation calculations. Thus, for example, in an adiabatic vapor-liquid flash, no attempt should be made iteratively to correct compositions (and K s) at current estimates of T and a before proceeding with the Newton-Raphson iteration. Similarly, in liquid-liquid separations, iterations on phase compositions at the current estimate of phase ratio (a)r or at some estimate of the conjugate phase composition, are almost always counterproductive. Each thermodynamic function evaluation (set of K ) should be used to improve estimates of all variables in the system. 

Liquid-liquid equilibrium separation calculations are superficially similar to isothermal vapor-liquid flash calculations. They also use the objective function. Equation (7-13), in a step-limited Newton-Raphson iteration for a, which is here E/F. However, because of the very strong dependence of equilibrium ratios on phase compositions, a computation as described for isothermal flash processes can converge very slowly, especially near the plait point. (Sometimes 50 or more iterations are required. )... 

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